Containers for cosmetic products such as mascara, eyeliner and the like traditionally have a built-in applicator wand, for example in the form of a narrow, elongate brush. Typically, the wand is attached to a closure for the container so that the wand fits within the container when the closure is in place. To apply the cosmetic, the closure is removed from the container, bringing with it the wand and a certain amount of the cosmetic, carried on the wand. An annular lip is provided within the container neck to act as a wiper against which the wand is drawn as it is removed from a container so that excess amounts of the cosmetic are removed from tho wand.